Question : A point D is taken from the side BC of a right-angled triangle ABC, where AB is hypotenuse. Then:
Option 1: AB2 + CD2 = BC2 + AD2
Option 2: CD2 + BD2 = 2AD2
Option 3: AB2 + AC2 = 2AD2
Option 4: AB2 = AD2 + BD2
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Correct Answer: AB 2 + CD 2 = BC 2 + AD 2
Solution :
According to the question,
Using Pythagoras theorem,
In $\triangle$ABC
AB
2
= AC
2
+ BC
2
...........................................(i)
In $\triangle$ACD
AD
2
= AC
2
+ CD
2
AC
2
= AD
2
– CD
2
...........................................(ii)
Put the value of AC
2
in equation (i)
AB
2
= AD
2
– CD
2
+ BC
2
AB
2
+ CD
2
= AD
2
+ BC
2
Hence, the correct answer is AB
2
+ CD
2
= BC
2
+ AD
2
.
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